Magnetism, superconductivity and their interaction in some condensed matter systems

This dissertation summarizes work on high T_c superconductors, conventional superconductors with magnetic impurities, and spin-polarized currents.; High T_c materials are superconductors at finite level of hole doping and antiferromagnetic insulators for zero doping. There is a lot of evidence that proximity to the antiferromagnetic state is required to obtain large T_c values. Here we developed two aspects of S. C. Zhang's SO(5) theory that unifies antiferromagnetism and superconductivity in cuprates. First, it is predicted that the so-called π-mode observed in neutron scattering experiments only below T_c should be also observable above T_c a the tunneling experiment. Second, the stripe phase of the high T_c superconductor is explained as a result of a competition between the short-range SO(5) symmetric interactions and the long-range electrostatic interaction.; Magnetic impurities destroy conventional superconductivity by creating an extra electron state inside the energy gap. It is known that the nature of this state will experience a transition as the impurity strength is increased. On the basis of the BCS theory we calculated the spatial spin density distribution near impurity as a function of its strength and showed that one Cooper pair is broken during the transition. It is also proposed how to mimic impurity strength variation in an experiment. Our results are relevant for the scanning tunneling microscope measurements of the local electronic structure near the impurity.; When ferromagnets are used as electric wires a spin-polarized current is created. Such current has properties unknown in the conventional electronics due to the angular momentum ħ/2 associated with each electron spin. The spin-transfer effect produced by motion and rotation of the spins starts to play a role for nano-scale devices with large current densities. We formulated a modified Landau-Lifshitz equation that accounts for this effect and solved it in several situations. Spin-transfer effect is capable of changing magnetic configuration of the sample. We investigated the possibility of using it as a writing process for the random-access memory based on arrays of miniature spin-valves.